Today, we solved a few more inverse trig problems. A couple of interesting topics arose.
The first slide shows an integral that required an inverse secant and substitution. Don't forget to change the limits of integration when you make your substitution.
The second slide shows a derivative of an inverse cosecant function that also requires the chain rule. Anto's solution involved inserting an x^4 inside a square root. (To explain this step, he showed an example of the technique in the upper right corner.) Can you see another way forward that avoids inserting x^4 inside the radical?
The last slide shows a definite integral of a rational function with trigonometric expressions in both the numerator and denominator. Juan used the wise step of doing some algebra before doing the calculus. This step avoids using any inverse trig functions. The problem is that he forgot to extract both the negative and positive roots. It turns out we only needed the negative root because in the interval [3,4], cosine is negative.
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Then we looked at the answers to the multiple choice questions from review sheets 1 & 2.
Be prepared on Wednesday to ask questions on any problems for which you have confusion or doubt.
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